In recent years, Sandryhaila and Moura generalized some fundamental concepts of traditional signal processing such as filtering to directed graphs using the adjacency matrix as the central component of their framework [1]}. They also proposed the generalized eigenvectors of the adjacency matrix obtained by Jordan decomposition as a Fourier-type basis on directed graphs [2]}. As far as we know, no wavelet design was developed in this framework, with the exception of the development of the filterbank approach generalized in [3]} which can be applied to bipartite directed graphs and uses the adjacency matrix for a polyphase representation of the filters.
